一类非线性二阶多点边值问题正解的存在性

The Existence of Positive Solution to the Problem of One Non-Linear Second Order Multipoint Boundary Value

讨论一类非线性二阶多点边值问题正解的存在性,利用上下解方法,通过定义适当的锥,运用锥映射的不动点定理,对已有的二阶三点边值问题的正解的结论进行推广,给出了二阶多点边值问题正解存在性的判定方法,从而获得了该类边值问题存在正解的结果.

To discuss the existence of positive solution to the problem of one non-linear second order multipoint boundary value, by application of upper and lower solutions, the definition of fixed cone and the application of the fixed point theorem of cone mapping to generalize the existed conclusion of positive solution of second order thirdpoint boundary value, giving decision method to the existence of positive solution to second order multipoint boundary value, inferring significant results of positive solution for such boundary value problem.